This module bundles some of the most important functionality
of the AERN-Real package. It is intended to be imported *qualified*.

AERN-Real provides
datatypes and abstractions for approximating exact real numbers
and a basic arithmetic over such approximations. The approach is
inspired to some degree by Mueller's iRRAM and Lambov's RealLib
(both are C++ libraries for exact real arithmetic).

ERIntApprox: abstracts neighbourhoods of real numbers that are known to be intervals

ERApproxElementary: abstracts real number approximations that support elementary operations

For ERRealBase we give several implementations. The default is
an arbitrary precision floating point type that uses Double
for lower precisions and an Integer-based simulation for higher
precisions. Rational numbers can be used as one of the alternatives.
Augustsson's Data.Number.BigFloat can be easily wrapped as an instance
of ERRealBase except that it uses a different method to control precision.

ERIntApprox is implemented via outwards-rounded arbitrary precision interval arithmetic.
Any instance of ERRealBase can be used for the endpoints of the intervals.

ERApproxElementary is implemented generically for any implementation
of ERIntApprox. This way some of the most common elementary operations are provided,
notably: sqrt, exp, log, sin, cos, atan. These operations converge
to an arbitrary precision and also work well over larger intervals without
excessive wrapping.

There is also some support for generic Taylor series, interval Newton method
and simple numerical integration.